PhD Chapter 1
Campaign 2017 - Analyses and regressions
This series of files compile analyses done for the specific analysis of Chapter 1, for the regional campaign of 2017.
All analyses have been done with PRIMER-e 6 and R 4.0.4.
Click on the table of contents in the left margin to assess a specific analysis.
Click on a figure to zoom it
We used data from subtidal ecosystems (see metadata files for more information). Only stations that have been sampled both for abiotic parameters and benthic species were included.
Selected variables for the analyses:
- Depth of the station: depth (only for ANCOVAs)
- Percentage of organic matter: om
- Percentage of gravel: gravel
- Percentage of sand: sand
- Percentage of silt: silt
- Percentage of clay: clay
- Concentration of arsenic: arsenic
- Concentration of cadmium: cadmium
- Concentration of chromium: chromium
- Concentration of copper: copper
- Concentration of iron: iron
- Concentration of manganese: manganese
- Concentration of mercury: mercury
- Concentration of lead: lead
- Concentration of zinc: zinc
- Specific richness: S(only for 500 µm communities)
- Total density of individuals: N (only for 500 µm communities)
- Shannon’s diversity: H (only for 500 µm communities)
- Piélou’s evenness: J (only for 500 µm communities)
We only considered 500 µm communities for these analyses. Abundances of Bipalponephtys neotena (Bneo) and Nematoda (Nema) were also considered (see IndVal and SIMPER results).
Heavy metal concentrations for campaign 2017 have been kriged from the values collected at campaigns 2014 and 2016. As data is missing for metal concentrations outside BSI, two Designs have been used:
- Design 1: stations at BSI, MR with habitat parameters
- Design 2: stations at BSI with heavy metal concentrations.
1. Permutational Analyses of Covariance
Results of univariate PermANCOVAs on parameters and multivariate PermANCOVA on the whole benthic community with depth as covariate are presented in the table below. Variables have been standardized by mean and standard-deviation, and taxon densities were (log+1) transformed.
| Variable | Condition | Depth |
|---|---|---|
| om | S | |
| gravel | ||
| sand | ||
| silt | S | |
| clay | ||
| S (500 µm) | S | |
| N (500 µm) | ||
| H (500 µm) | S | |
| J (500 µm) | S | |
| ALL SPECIES (500 µm) | S | S |
2. Similarity and characteristic species
Let’s have a look at the \(\beta\) diversity within our conditions and sites.
Results of the PERMDISP routine are shown below (mean and SE of the deviation from centroid for each group, i.e. multivariate dispersion), along with the mean Bray-Curtis dissimilarity for each group. Taxon densities were (log+1) transformed and PRIMER was used to do the PERMDISP.
| Mean deviation | SE of deviation | Mean BC dissimilarity | |
|---|---|---|---|
| HI | 57.5 | 1.64 | 0.829 |
| R | 48.8 | 2.43 | 0.71 |
Significative differences in dispersion have been detected between HI and R (p = 0.0053).
The following analyses allowed to detect species as characteristic of each condition. We used results from PRIMER to justify further their choice.
## cluster indicator_value probability
## bipalponephtys_neotena 1 0.6390 0.001
## macoma_calcarea 1 0.5583 0.004
## goniada_maculata 1 0.2917 0.028
## nematoda 2 0.6565 0.005
## echinarachnius_parma 2 0.6524 0.001
## crenella_decussata 2 0.5836 0.001
## ecrobia_truncata 2 0.3333 0.005
## mesodesma_arctatum 2 0.2667 0.016
## solariella_sp 2 0.2000 0.039
##
## Sum of probabilities = 55.401
##
## Sum of Indicator Values = 13.26
##
## Sum of Significant Indicator Values = 4.18
##
## Number of Significant Indicators = 9
##
## Significant Indicator Distribution
##
## 1 2
## 3 6
| average | sd | ratio | ava | avb | cumsum | |
|---|---|---|---|---|---|---|
| nematoda | 0.0743 | 0.0621 | 1.2 | 0.879 | 2.08 | 0.0852 |
| echinarachnius_parma | 0.0618 | 0.0632 | 0.977 | 0.361 | 1.59 | 0.156 |
| bipalponephtys_neotena | 0.0556 | 0.0485 | 1.15 | 1.78 | 0.193 | 0.22 |
| eudorellopsis_integra | 0.0358 | 0.0494 | 0.724 | 1.08 | 0.119 | 0.261 |
| crenella_decussata | 0.0346 | 0.0352 | 0.983 | 0.0289 | 1.03 | 0.3 |
| mesodesma_arctatum | 0.0338 | 0.064 | 0.528 | 0 | 0.751 | 0.339 |
| macoma_calcarea | 0.0316 | 0.0323 | 0.977 | 1.03 | 0.0462 | 0.375 |
| harpacticoida | 0.0283 | 0.0325 | 0.872 | 0.801 | 0.258 | 0.408 |
| phoxocephalus_holbolli | 0.0282 | 0.0329 | 0.857 | 0.411 | 0.658 | 0.44 |
| amphipoda | 0.0234 | 0.0274 | 0.852 | 0.483 | 0.346 | 0.467 |
| pholoe_sp | 0.0215 | 0.0249 | 0.866 | 0.413 | 0.434 | 0.492 |
| ameritella_agilis | 0.018 | 0.0252 | 0.715 | 0.132 | 0.451 | 0.512 |
| ecrobia_truncata | 0.0168 | 0.0321 | 0.525 | 0 | 0.575 | 0.532 |
| ennucula_tenuis | 0.0164 | 0.022 | 0.742 | 0.401 | 0.212 | 0.55 |
| ischyrocerus_anguipes | 0.0155 | 0.0327 | 0.475 | 0.406 | 0.13 | 0.568 |
| akanthophoreus_gracilis | 0.0154 | 0.0263 | 0.584 | 0.389 | 0.193 | 0.586 |
| hiatella_arctica | 0.015 | 0.0309 | 0.483 | 0.0747 | 0.368 | 0.603 |
| ostracoda | 0.013 | 0.0195 | 0.664 | 0.207 | 0.258 | 0.618 |
| cistenides_granulata | 0.0129 | 0.0202 | 0.641 | 0.233 | 0.212 | 0.633 |
| axinopsida_orbiculata | 0.0117 | 0.025 | 0.47 | 0.361 | 0 | 0.646 |
| thracia_septentrionalis | 0.0117 | 0.0185 | 0.633 | 0.183 | 0.266 | 0.66 |
| mysella_planulata | 0.0117 | 0.0263 | 0.445 | 0 | 0.333 | 0.673 |
| sabellidae_spp | 0.0112 | 0.0323 | 0.348 | 0.361 | 0.0462 | 0.686 |
| leucon_leucon_nasicoides | 0.0107 | 0.0237 | 0.454 | 0.294 | 0 | 0.698 |
| nephtyidae_spp | 0.0107 | 0.0176 | 0.608 | 0.274 | 0.0462 | 0.71 |
| orchomenella_minuta | 0.0102 | 0.019 | 0.539 | 0.0578 | 0.212 | 0.722 |
| nephtys_caeca | 0.00966 | 0.0194 | 0.497 | 0.116 | 0.119 | 0.733 |
| goniada_maculata | 0.00965 | 0.0165 | 0.585 | 0.286 | 0 | 0.744 |
| mytilus_sp | 0.0092 | 0.0268 | 0.342 | 0.287 | 0 | 0.755 |
| solariella_sp | 0.0089 | 0.0205 | 0.435 | 0 | 0.29 | 0.765 |
| pontoporeia_femorata | 0.00864 | 0.0245 | 0.352 | 0.225 | 0 | 0.775 |
| parvicardium_pinnulatum | 0.00863 | 0.0164 | 0.527 | 0.0578 | 0.227 | 0.785 |
| caprella_septentrionalis | 0.00844 | 0.029 | 0.291 | 0.34 | 0 | 0.795 |
| protomedeia_fasciata | 0.00786 | 0.0165 | 0.478 | 0.241 | 0 | 0.804 |
| lamprops_fuscatus | 0.00694 | 0.0128 | 0.543 | 0.207 | 0.0462 | 0.811 |
| pholoe_longa | 0.00605 | 0.0189 | 0.319 | 0.11 | 0.0732 | 0.818 |
| protomedeia_grandimana | 0.00592 | 0.0173 | 0.342 | 0.213 | 0 | 0.825 |
| astarte_sp | 0.00588 | 0.013 | 0.454 | 0.0747 | 0.119 | 0.832 |
| chone_sp | 0.00567 | 0.0282 | 0.201 | 0.107 | 0 | 0.838 |
| monoculopsis_longicornis | 0.00559 | 0.0144 | 0.388 | 0.125 | 0.0924 | 0.845 |
| ophelia_limacina | 0.00551 | 0.0112 | 0.494 | 0.0289 | 0.166 | 0.851 |
| glycera_sp | 0.00542 | 0.0171 | 0.317 | 0.116 | 0 | 0.857 |
| chaetodermatida | 0.00541 | 0.0117 | 0.462 | 0.144 | 0.0462 | 0.864 |
| nephtys_incisa | 0.00535 | 0.0126 | 0.423 | 0.104 | 0.0462 | 0.87 |
| maldanidae_spp | 0.00472 | 0.0156 | 0.303 | 0.113 | 0.0462 | 0.875 |
| aceroides_aceroides_latipes | 0.00452 | 0.0111 | 0.406 | 0.144 | 0 | 0.88 |
| quasimelita_formosa | 0.00447 | 0.0122 | 0.366 | 0.125 | 0 | 0.885 |
| sipuncula | 0.00428 | 0.0122 | 0.35 | 0 | 0.0924 | 0.89 |
| euchone_sp | 0.00426 | 0.0207 | 0.206 | 0.146 | 0 | 0.895 |
| anthozoa | 0.00409 | 0.0111 | 0.369 | 0 | 0.119 | 0.9 |
3. Regressions
3.1. Data manipulation
For the following analyses, independant variables are habitat parameters and heavy metal concentrations, dependant variables are diversity indices. Variables have been standardized by mean and standard-deviation.
3.1.1. Identification of outliers
To identify stations that are not consistent with the others, we used the multivariate Cook’s Distance (CD) on the uncorrelated variables. A significative threshold of 4 times the mean of CD has been established.
Design 1
We identified stations 188, 194 and 228 as general outliers. They have been deleted for the following analyses of Design 1.
Design 2
We identified stations 132 and 154 as general outliers. They have been deleted for the following analyses of Design 2.
3.1.2. Correlations between predictors
Correlations have been calculated with Spearman’s rank coefficient.
Design 1
According to these results, the following variables are highly correlated (\(|\rho|\) > 0.80) so they have been considered together in the regressions of Design 1:
- sand and silt (silt deleted)
| om | gravel | sand | silt | clay | |
|---|---|---|---|---|---|
| om | 1 | -0.365 | -0.791 | 0.877 | 0.119 |
| gravel | -0.365 | 1 | 0.015 | -0.325 | 0.183 |
| sand | -0.791 | 0.015 | 1 | -0.896 | -0.47 |
| silt | 0.877 | -0.325 | -0.896 | 1 | 0.212 |
| clay | 0.119 | 0.183 | -0.47 | 0.212 | 1 |
Design 2
Many variables are highly correlated (\(|\rho|\) > 0.80), but we have considered the following together in the regressions of Design 2:
- chromium, iron and manganese (iron and manganese deleted)
- copper, lead and zinc (copper and zinc deleted)
We decided to keep arsenic, even though it is correlated with the copper/lead/zinc group, to stay consistant with the 2014 and 2016 campaigns.
| arsenic | cadmium | chromium | copper | iron | manganese | mercury | lead | zinc | |
|---|---|---|---|---|---|---|---|---|---|
| arsenic | 1 | 0.658 | 0.838 | 0.801 | 0.701 | 0.598 | 0.438 | 0.8 | 0.874 |
| cadmium | 0.658 | 1 | 0.809 | 0.467 | 0.719 | 0.794 | 0.288 | 0.806 | 0.777 |
| chromium | 0.838 | 0.809 | 1 | 0.811 | 0.871 | 0.84 | 0.406 | 0.889 | 0.945 |
| copper | 0.801 | 0.467 | 0.811 | 1 | 0.688 | 0.573 | 0.308 | 0.805 | 0.896 |
| iron | 0.701 | 0.719 | 0.871 | 0.688 | 1 | 0.834 | 0.182 | 0.71 | 0.848 |
| manganese | 0.598 | 0.794 | 0.84 | 0.573 | 0.834 | 1 | 0.208 | 0.679 | 0.77 |
| mercury | 0.438 | 0.288 | 0.406 | 0.308 | 0.182 | 0.208 | 1 | 0.488 | 0.37 |
| lead | 0.8 | 0.806 | 0.889 | 0.805 | 0.71 | 0.679 | 0.488 | 1 | 0.924 |
| zinc | 0.874 | 0.777 | 0.945 | 0.896 | 0.848 | 0.77 | 0.37 | 0.924 | 1 |
3.2. Univariate regressions
We used linear models for the regressions on diversity indices. Outliers and correlated variables were removed from these analyses. Variables have been standardized by mean and standard-deviation (coefficients need to be back-transformed to be used in predictive models).
3.2.1. Simple regressions
These analyses have been do to explore the relationships between variables. As it is a huge number of results to interpret, only multiple regressions will be included in the article (see below).
Depth has been shown important for several parameters in the ANCOVAs, so here are the corresponding scatterplots.
Design 1
| om | gravel | sand | clay | |
|---|---|---|---|---|
| S_500 | -0.02767 | 0.01197 | -0.001571 | -0.02831 |
| N_500 | -0.0185 | -0.02098 | -0.02294 | 0.002618 |
| H_500 | -0.009374 | -0.0139 | 0.02245 | 0.02041 |
| J_500 | 0.02241 | -0.02941 | 0.005738 | 0.02843 |
| om | gravel | sand | clay | |
|---|---|---|---|---|
| S_500 | 0.8117 | 0.241 | 0.3378 | 0.8497 |
| N_500 | 0.5501 | 0.5997 | 0.6458 | 0.3034 |
| H_500 | 0.417 | 0.4757 | 0.1882 | 0.1973 |
| J_500 | 0.1883 | 0.9884 | 0.2806 | 0.1639 |
Design 2
Quitting from lines 273-287 (C1_analyses_17B.Rmd) Error in pandoc.table.return(…) : Wrong number of parameters (7 instead of 6) passed: justify De plus : Warning messages: 1: attribute variables are assumed to be spatially constant throughout all geometries 2: attribute variables are assumed to be spatially constant throughout all geometries 3: attribute variables are assumed to be spatially constant throughout all geometries 4: attribute variables are assumed to be spatially constant throughout all geometries 5: attribute variables are assumed to be spatially constant throughout all geometries 6: attribute variables are assumed to be spatially constant throughout all geometries 7: attribute variables are assumed to be spatially constant throughout all geometries 8: attribute variables are assumed to be spatially constant throughout all geometries Quitting from lines 273-287 (C1_analyses_17B.Rmd) Error in pandoc.table.return(…) : Wrong number of parameters (7 instead of 6) passed: justify
3.2.2. Multiple regressions
This section presents analyses done to determine which variables are the most important to explain the parameters.
We identified which variables were selected after an AIC procedure to predict the best the parameters. Results of the variable selection, according to AIC, are shown on the tables below:
- for the model of Design 1
| Variable (or combination) | S_500 | N_500 | H_500 | J_500 |
|---|---|---|---|---|
| om | + | |||
| gravel | + | |||
| sand/silt | + | |||
| clay | + | |||
| Adjusted \(R^{2}\) | 0 | 0 | 0 | 0.06 |
- for the model of Design 2
| Variable (or combination) | S_500 | N_500 | H_500 | J_500 |
|---|---|---|---|---|
| arsenic | - | - | - | |
| cadmium | + | |||
| chromium/iron/manganese | - | - | - | |
| mercury | - | - | ||
| lead/copper/zinc | + | + | + | |
| Adjusted \(R^{2}\) | 0.24 | 0.26 | 0.24 | 0.09 |
Details of the regressions, with diagnostics and cross-validation, are summarized below.
Design 1
Richness
## FULL MODEL
## Adjusted R2 is: -0.06
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.09546 | 0.1757 | 0.5434 | 0.5907 | |
| om | -0.2095 | 0.5347 | -0.3918 | 0.6979 | |
| gravel | 0.07971 | 0.2617 | 0.3046 | 0.7627 | |
| sand | -0.3523 | 0.5343 | -0.6593 | 0.5146 | |
| clay | -0.1332 | 0.2967 | -0.4489 | 0.6566 |
## RMSE from cross-validation: 10.96324
| om | gravel | sand | clay | |
|---|---|---|---|---|
| VIF | 2.3 | 1.55 | 2.93 | 1.76 |
## REDUCED MODEL
## Adjusted R2 is: 0
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.07403 | 0.1675 | 0.4419 | 0.6613 |
## RMSE from cross-validation: 0.9974367
Quitting from lines 330-332 (C1_analyses_17B.Rmd) Error in Qr\(qr[p1, p1, drop = FALSE] : indice hors limites De plus : Warning messages: 1: In CVlm(data = lm_out\)model, form.lm = lm_out, m = 5, printit = F) :
As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate
2: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :
As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate
Density
## FULL MODEL
## Adjusted R2 is: -0.06
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.03898 | 0.1774 | 0.2197 | 0.8275 | |
| om | -0.4389 | 0.54 | -0.8128 | 0.4225 | |
| gravel | -0.07614 | 0.2642 | -0.2882 | 0.7751 | |
| sand | -0.3968 | 0.5396 | -0.7354 | 0.4676 | |
| clay | -0.34 | 0.2996 | -1.135 | 0.2652 |
## RMSE from cross-validation: 17.81878
| om | gravel | sand | clay | |
|---|---|---|---|---|
| VIF | 2.3 | 1.55 | 2.93 | 1.76 |
## REDUCED MODEL
## Adjusted R2 is: 0
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.0233 | 0.1689 | 0.1379 | 0.8911 |
## RMSE from cross-validation: 1.082179
Quitting from lines 342-344 (C1_analyses_17B.Rmd) Error in Qr\(qr[p1, p1, drop = FALSE] : indice hors limites De plus : Warning messages: 1: In CVlm(data = lm_out\)model, form.lm = lm_out, m = 5, printit = F) :
As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate
2: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :
As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate
Diversity
## FULL MODEL
## Adjusted R2 is: -0.03
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.05635 | 0.1667 | 0.3381 | 0.7376 | |
| om | 0.4183 | 0.5073 | 0.8246 | 0.4159 | |
| gravel | 0.2463 | 0.2483 | 0.9921 | 0.3288 | |
| sand | 0.2698 | 0.507 | 0.5323 | 0.5983 | |
| clay | 0.3124 | 0.2815 | 1.11 | 0.2756 |
## RMSE from cross-validation: 27.97158
| om | gravel | sand | clay | |
|---|---|---|---|---|
| VIF | 2.3 | 1.55 | 2.93 | 1.76 |
## REDUCED MODEL
## Adjusted R2 is: 0
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.06334 | 0.1616 | 0.392 | 0.6975 |
## RMSE from cross-validation: 0.9736631
Quitting from lines 354-356 (C1_analyses_17B.Rmd) Error in Qr\(qr[p1, p1, drop = FALSE] : indice hors limites De plus : Warning messages: 1: In CVlm(data = lm_out\)model, form.lm = lm_out, m = 5, printit = F) :
As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate
2: In CVlm(data = lm_out$model, form.lm = lm_out, m = 5, printit = F) :
As there is >1 explanatory variable, cross-validation predicted values for a fold are not a linear function of corresponding overall predicted values. Lines that are shown for the different folds are approximate
Evenness
## FULL MODEL
## Adjusted R2 is: 0.06
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.006409 | 0.1518 | 0.04221 | 0.9666 | |
| om | 0.9141 | 0.4621 | 1.978 | 0.05686 | |
| gravel | 0.3201 | 0.2262 | 1.415 | 0.1669 | |
| sand | 0.7476 | 0.4618 | 1.619 | 0.1156 | |
| clay | 0.5227 | 0.2564 | 2.038 | 0.05012 |
## RMSE from cross-validation: 26.77056
| om | gravel | sand | clay | |
|---|---|---|---|---|
| VIF | 2.3 | 1.55 | 2.93 | 1.76 |
## REDUCED MODEL
## Adjusted R2 is: 0.06
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.006409 | 0.1518 | 0.04221 | 0.9666 | |
| om | 0.9141 | 0.4621 | 1.978 | 0.05686 | |
| gravel | 0.3201 | 0.2262 | 1.415 | 0.1669 | |
| sand | 0.7476 | 0.4618 | 1.619 | 0.1156 | |
| clay | 0.5227 | 0.2564 | 2.038 | 0.05012 |
## RMSE from cross-validation: 26.77056
| om | gravel | sand | clay | |
|---|---|---|---|---|
| VIF | 2.3 | 1.55 | 2.93 | 1.76 |
Design 2
Richness
## FULL MODEL
## Adjusted R2 is: 0.21
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.2519 | 0.2374 | -1.061 | 0.3045 | |
| arsenic | -1.006 | 0.7414 | -1.356 | 0.1938 | |
| cadmium | -0.1794 | 0.3118 | -0.5752 | 0.5731 | |
| chromium | -0.6905 | 0.6333 | -1.09 | 0.2917 | |
| mercury | -0.6837 | 0.489 | -1.398 | 0.1812 | |
| lead | 1.029 | 0.7637 | 1.347 | 0.1966 |
## RMSE from cross-validation: 1.145083
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 2.11 | 1.6 | 3.14 | 1.22 | 3.69 |
## REDUCED MODEL
## Adjusted R2 is: 0.24
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.247 | 0.2326 | -1.062 | 0.3031 | |
| arsenic | -1.014 | 0.7265 | -1.396 | 0.1807 | |
| chromium | -0.8021 | 0.5908 | -1.358 | 0.1923 | |
| mercury | -0.6267 | 0.4693 | -1.335 | 0.1994 | |
| lead | 0.985 | 0.7447 | 1.323 | 0.2035 |
## RMSE from cross-validation: 1.012635
| arsenic | chromium | mercury | lead | |
|---|---|---|---|---|
| VIF | 2.11 | 2.99 | 1.2 | 3.67 |
Density
## FULL MODEL
## Adjusted R2 is: 0.18
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.2115 | 0.2383 | -0.8875 | 0.3879 | |
| arsenic | -0.6111 | 0.7441 | -0.8212 | 0.4236 | |
| cadmium | 0.4067 | 0.3129 | 1.3 | 0.2121 | |
| chromium | -0.07125 | 0.6356 | -0.1121 | 0.9121 | |
| mercury | -0.7709 | 0.4908 | -1.571 | 0.1358 | |
| lead | -0.1252 | 0.7665 | -0.1633 | 0.8723 |
## RMSE from cross-validation: 1.056123
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 2.11 | 1.6 | 3.14 | 1.22 | 3.69 |
## REDUCED MODEL
## Adjusted R2 is: 0.26
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.2439 | 0.2092 | -1.166 | 0.2589 | |
| arsenic | -0.8016 | 0.4748 | -1.688 | 0.1086 | |
| cadmium | 0.3459 | 0.2472 | 1.399 | 0.1788 | |
| mercury | -0.8427 | 0.4205 | -2.004 | 0.06036 |
## RMSE from cross-validation: 0.9536134
| arsenic | cadmium | mercury | |
|---|---|---|---|
| VIF | 1.42 | 1.33 | 1.11 |
Diversity
## FULL MODEL
## Adjusted R2 is: 0.24
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.2432 | 0.2299 | -1.058 | 0.3059 | |
| arsenic | -1.098 | 0.7179 | -1.529 | 0.1458 | |
| cadmium | -0.2655 | 0.3019 | -0.8792 | 0.3923 | |
| chromium | -1.18 | 0.6132 | -1.924 | 0.07233 | |
| mercury | -0.604 | 0.4735 | -1.276 | 0.2203 | |
| lead | 1.745 | 0.7395 | 2.359 | 0.03135 | * |
## RMSE from cross-validation: 1.218505
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 2.11 | 1.6 | 3.14 | 1.22 | 3.69 |
## REDUCED MODEL
## Adjusted R2 is: 0.24
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | -0.1355 | 0.2117 | -0.6398 | 0.5304 | |
| arsenic | -1.021 | 0.7139 | -1.43 | 0.1698 | |
| chromium | -1.287 | 0.5819 | -2.212 | 0.04012 | * |
| lead | 1.434 | 0.7029 | 2.04 | 0.05632 |
## RMSE from cross-validation: 0.9705081
| arsenic | chromium | lead | |
|---|---|---|---|
| VIF | 2.09 | 2.98 | 3.51 |
Evenness
## FULL MODEL
## Adjusted R2 is: -0.07
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.0006482 | 0.2717 | 0.002385 | 0.9981 | |
| arsenic | -0.2288 | 0.8484 | -0.2697 | 0.7908 | |
| cadmium | -0.04213 | 0.3568 | -0.1181 | 0.9075 | |
| chromium | -1.262 | 0.7247 | -1.741 | 0.1008 | |
| mercury | 0.04122 | 0.5595 | 0.07367 | 0.9422 | |
| lead | 1.368 | 0.8739 | 1.565 | 0.1371 |
## RMSE from cross-validation: 1.475412
| arsenic | cadmium | chromium | mercury | lead | |
|---|---|---|---|---|---|
| VIF | 2.11 | 1.6 | 3.14 | 1.22 | 3.69 |
## REDUCED MODEL
## Adjusted R2 is: 0.09
| Estimate | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|
| (Intercept) | 0.01992 | 0.2107 | 0.09453 | 0.9257 | |
| chromium | -1.294 | 0.6326 | -2.045 | 0.055 | |
| lead | 1.259 | 0.6494 | 1.938 | 0.06757 |
## RMSE from cross-validation: 1.348883
| chromium | lead | |
|---|---|---|
| VIF | 2.98 | 2.98 |
3.3. Multivariate regressions
Independant variables are habitat parameters or heavy metal concentrations, dependant variables are species abundances. Variables have been standardized by mean and standard-deviation, and outliers and correlated variables have been excluded. Taxon densities were (log+1) transformed.
This analysis has been done on PRIMER, with a DistLM to identify the variables that explain the most the community variability and with a dbRDA to plot the results.
Design 1
Variables selected by the DistLM procedure have a \(R^{2}\) of 0.23.
Design 2
Variables selected by the DistLM procedure have a \(R^{2}\) of 0.13.